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Arc spaces and singularities in the minimal model program - Lecture 1
Post-edited
Authors : de Fernex, Tommaso (Author of the conference)
CIRM (Publisher )
13A18 - Valuations and their generalizations [See also 12J20]
14B05 - Singularities
14E15 - Global theory and resolution of singularities
14E30 - Minimal model program (Mori theory, extremal rays)
14E18 - Arcs and motivic integration
CIRM (Publisher )
Abstract :
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.
MSC Codes : 13A18 - Valuations and their generalizations [See also 12J20]
14B05 - Singularities
14E15 - Global theory and resolution of singularities
14E30 - Minimal model program (Mori theory, extremal rays)
14E18 - Arcs and motivic integration
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 26/02/15 Conference Date : 09/02/15 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : QuickTime (.mov) Video Time : 01:02:02 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-02-09_Fernex_part1.mp4 
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Information on the Event
Event Title : Young researchers in singularities / Jeunes chercheurs en singularitésEvent Organizers : Fichou, Goulwen ; Plénat, Camille Dates : 09/02/15 - 13/02/15 Event Year : 2015 Event URL : http://chairejeanmorlet-1stsemester2015....
Citation Data
DOI : 10.24350/CIRM.V.18697103Cite this video as: de Fernex, Tommaso (2015). Arc spaces and singularities in the minimal model program - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18697103 URI : http://dx.doi.org/10.24350/CIRM.V.18697103 |
See Also
- [Multi angle] Arc spaces and singularities in the minimal model program - Lecture 4 / Author of the conference de Fernex, Tommaso.
- [Multi angle] Arc spaces and singularities in the minimal model program - Lecture 3 / Author of the conference de Fernex, Tommaso.
- [Multi angle] Arc spaces and singularities in the minimal model program - Lecture 2 / Author of the conference de Fernex, Tommaso.
Bibliography
- [1] de Fernex, T. (2013). Three-dimensional counter-examples to the Nash problem. Compositio Mathematica, 149(9), 1519-1534 - http://dx.doi.org/10.1112/S0010437X13007252
- [2] de Fernex, T., & and Docampo, R. (2014). Terminal valuations and the Nash problem.
- [3] Ein, L., Lazarsfeld, R., & Mustata, M. (2004). Contact loci in arc spaces. Compositio Mathematica, 140(5), 1229-1244 - http://dx.doi.org/10.1112/S0010437X04000429
- [4] Ein, L., Mustata, M., & Yasuda, T. (2003). Jet schemes, log discrepancies and inversion of adjunction. Inventiones Mathematicae, 153(3), 519-535 - http://dx.doi.org/10.1007/s00222-003-0298-3
- [5] Fernández de Bobadilla, J., & Pe Pereira, M. (2012). The Nash problem for surfaces. Annals of Mathematics. Second Series, 176(3), 2003-2029 - http://dx.doi.org/10.4007/annals.2012.176.3.11
- [6] Ishii, S., & Kollár, J. (2003). The Nash problem on arc families of singularities. Duke Mathematical Journal, 120(3), 601-620 - http://dx.doi.org/10.1215/S0012-7094-03-12034-7
- [7] Nash, John F. jun. (1995). Arc structure of singularities. Duke Mathematical Journal, 81(1), 31-38 - http://dx.doi.org/10.1215/S0012-7094-95-08103-4
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